DMW Deemster, with roof! 1966-ish
OK, the DMW Deemster is not really an FF, but it was pretty innovative for the time, and civilised, and it was British, by George! Made in the West Midlands and powered by a British VIlliers 250cc twin-cylinder 2-stroke engine, it also came with a luxurious electric start, when almost all bikes and scooters were still strictly kick only. A cross between a motorcycle and a scooter, with big scooter wheels but a non-scooterish spine frame. Lots were sold to the police, for whom it was apparently developed, including 8 to the nearby Wolverhampton rozzers.
I don't know how common the roof was - most seemed to come with just the fairing and screen.
This one is pictured with an AA patrolman in Colwyn Bay, North Wales. Photo credit: Brian Shaw.
More information here: http://www.historywebsite.co.uk/Museum/Transport/Motorcycles/DMWmachines1.htm
PNB
Is this where academics go 'QED'?
Perfect illustration of why this sort of bodywork doesn't work untill you lower the rider enough to reduce frontal area.
Hint for designers. Start with a list of desirable features, then, using physics, work steadily towards the vehicle that embodies them. DO NOT start with a motorised bicycle and tack a list of desirable features onto it. That is provably a mistake.
It's the same mistake as the one involving pigs and lipstick. Or turds and polish.